Using the z-distribution, it is found that since the p-value of the test is less than 0.01, there is enough evidence to conclude that survival rates are different for day and night.
What are the hypothesis tested?
At the null hypothesis, it is tested if the proportions are the same, that is, the subtraction of them is 0, hence:
[tex]H_0: p_D - p_N = 0[/tex]
At the alternative hypothesis, it is tested if the proportions are different, that is:
[tex]H_1: p_D - p_N \neq 0[/tex]
What are the mean and the standard error for the distribution of differences?
For each sample, they are given as follows:
- [tex]p_D = \frac{23549}{43592} = 0.5402, s_D = \sqrt{\frac{0.5402(0.4598)}{43592}} = 0.0024[/tex]
- [tex]p_N = \frac{7804}{27963} = 0.2791, s_N = \sqrt{\frac{0.2791(0.6209)}{27963}} = 0.0025[/tex]
Hence, for the distribution of differences, they are given by:
- [tex]\overline{p} = p_D - p_N = 0.5402 - 0.2791 = 0.2611[/tex]
- [tex]s = \sqrt{s_D^2 + s_N^2} = \sqrt{0.0024^2 + 0.0025^2} = 0.0035[/tex].
What is the test statistic?
The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which p = 0 is the value tested at the null hypothesis.
Hence:
z = 0.2611/0.0035
z = 74.6.
What is the p-value of the test?
Using a z-distribution calculator, with z = 74.6, with a two-tailed test, as we are testing if the proportion is different of a value, the p-value is of 0.
Since the p-value of the test is less than 0.01, there is enough evidence to conclude that survival rates are different for day and night.
More can be learned about the z-distribution at https://brainly.com/question/13873630
#SPJ1
